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A Comprehensive Review on Image Restoration Techniques
Biswa Ranjan Mohapatra, Ansuman Mishra, Sarat Kumar Rout
Department of CSE, BIET, Bhadrak Odisha
Abstract- Image restoration is an art to improve the quality of image via estimating the amount of noises and blur involved in the image. With the passage of time, image gets degraded due to different atmospheric and environmental conditions, so it is required to restore the original image using different image processing algorithms. There is a wide spread application of image restoration in today’s world. Application area varies from restoration of old images in museum and radar based image acquisition and restoration. This paper gives a review of different image restoration techniques used.
Keywords- Blur, image restoration, image acquisition 1. INTRODUCTION
Image restoration is based on the attempt to improve the quality of an image through knowledge of the physical process which led to its formation. The purpose of image restoration is to "compensate for" or "undo" defects which degrade an image. Degradation comes in many forms such as motion blur, noise, and camera mis-focus. In cases like motion blur, it is possible to come up with a very good estimate of the actual blurring function and "undo" the blur to restore the original image. In cases where the image is corrupted by noise, the best we may hope to do is to compensate for the degradation it caused. Image restoration differs from image enhancement in that the latter is concerned more with accentuation or extraction of image features rather than restoration of degradations. Image restoration problems can be quantified precisely, whereas enhancement criteria are difficult to represent mathematically.
Image restoration started in 1950’s. There are several application domain of image restoration like scientific exploration, legal investigations, film making and archivals, image and video decoding and consumer photography. The main area of application is image reconstruction in radio astronomy, radar imaging and tomography.
This paper discusses the importance of image restoration techniques and reviews different image restoration techniques available.
2. IMAGE RESTORATION
Image restoration uses a priori knowledge of the degradation. It models the degradation and applies inverse process. It formulates and evaluates the objective criteria of goodness. The distortion can be modelled as noise or a degradation function. To restore an image from a noise model, different filters like median filter, homomorphic filters are used. To get rid of periodic noises, butterworth lowpass filter, butterworth band reject filters and notch filters are used. To restore an image from linear degradation, inverse and pseudo inverse filtering, wiener filtering and blind de-convolution are used.
A simplified version for the image restoration process model is
y i j
( )
,
=
H
f i j
( )
,
+
n i j
( )
,
(1)Where
y i j
( )
,
is the degraded image,f i j
( )
,
is the original image,H
an operator that represents the degradation process,( )
,
n i j
the external noise which is assumed to be image-independent.Figure 1: Image degradation and restoration techniques
Noise Models
In image processing there are different noise models available.
Gaussian Noise can be represented as
( )
( )Rayeligh’s noise can be represented as
( )
(
)
( )Salt and Pepper noise can be represented as
( )
a(
)
b(
)
p z
=
P
δ
z
− +
a
P
δ
z b
−
(4)There are different kinds of blurs involved in images some of the blurs are discussed below.
Blur Models
Motion blur occurs when there is relative motion between the object and the camera during exposure. This can be in the form of a translation, a rotation, a sudden change of scale, or some combinations of these.
( )
1
2
2
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When a camera images a 3-D scene onto a 2-D imaging plane, some parts of the scene are in focus while other parts are not. If the aperture of the camera is circular, the image of any point source is a small disk, known as the circle of confusion (COC). The degree of defocus (diameter of the COC) depends on the focal length and the aperture number of the lens, and the distance between camera and object. An accurate model not only describes the diameter of the COC, but also the intensity distribution within the COC. However, if the degree of defocusing is large relative to the wavelengths considered, a geometrical approach can be followed resulting in a uniform intensity distribution within the COC. Uniform out of focus
Uniform 2-D blur is defined by
( )
2 describes the degradation model.( ) ( )
2 (ISNR) validates the performance of the image restoration algorithm.original Image median filtered Image
Figure 2: Noisy Image and Median filtered image
original Image median filtered Image
median filter restoration
Figure 3: Image degradation and restoration techniques
Figure 3 show the same noisy image heavily corrupted by salt and pepper noise and median filter of window size (9x9) is used. The higher the window size of median filter there is a higher chance of image degradation.
Table 1: PSNR value (dB) for % of salt and pepper noise (Image: Cameraman, Filter: Median)
10% 20% 50% 90% 1 MF (3X3) 33.7 27.28 14.12 6.54 2 MF (5X5) 31.44 30.67 12.88 7.29 3 MF (9X9) 29.47 28.99 16.54 8.09
To restore an image from linear degradation inverse filter, pseudo inverse filter, Weiner filter and blind de-convolution is used. These techniques are discussed below.
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Degraded Image Restored Image
Figure 4: Image degradation and restoration using inverse filter
Pseudo Inverse Filter
Pseudo inverse filter can be expressed as
( )
( )
( )
Degraded Image Restored Image
Figure 5: Image degradation and restoration using pseudo inverse filter
Blurred Image
show noisy with degraded image
pseudo-inverse restoration
Figure 6: Image degradation and restoration using pseudo inverse filter
Weiner Filter
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Restoration of Blurred, Noisy Image Using Estimated NSR
Restoration of Blurred, Quantized Image Using Computed NSR
wiener filter restoration
Figure 7: Image degradation and restoration using Weiner filter
Geometric Mean Filter
Geometric mean filter is the generalization form of Weiner filter. The mathematical expression of geometric mean filter is defined as
( )
( )
( )
( )
( )
( )
( )
( )
1
2
2
, ,
, ,
, ,
,
,
n f
H u v H u v
F u v G u v
S u v
H u v
H u v
S u v
α α
β
−
=
+
(14)
Geometric Mean filter restoration
Figure 8: Image degradation and restoration using geometric mean filter restoration
Blind Deconvolution Algorithm
The Blind Deconvolution Algorithm can be used effectively when no information about the distortion (blurring and noise) is known. The algorithm restores the image and the point-spread function (PSF) simultaneously. The accelerated, damped Richardson-Lucy algorithm is used in each iteration. Additional optical system (e.g. camera) characteristics can be used as input parameters that could help to improve the quality of the image restoration. Blind deconvolution is the problem of recovering a sharp version of an input blurry image when the blur kernel is unknown. Mathematically
y
= ⊗
k
x
Where x is a visually plausible sharp image, and k is a non negative blur kernel, whose support is small compared to the image size.
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Deblurring with Undersized PSF
Deblurring with Oversized PSF
Deblurring with INITPSF
Figure 9: Image degradation and restoration using blind deconvolution algorithm
Richardson-Lucy Deconvolution Algorithm
The Richardson–Lucy deconvolution algorithm has become popular in the fields of astronomy and medical imaging. Initially it was derived from Bayes’s theorem in the early 1970’s by Richardson and Lucy.
Pixels in the observed image can be represented by
i ij j j
d
=
∑
p u
(15)
1
t t i j j ij
i i
d
u
u
p
c
+
=
∑
(16)1
ˆ
t t j j t
d
u
u
p
u
p
+
=
⊗
⊗
(17)
A = Blurred and Noisy deconvlucy(A,PSF)
deconvlucy(A,PSF,NI,DP) deconvlucy(A,PSF,NI,DP,WT)
Figure 10: Image degradation and restoration using Richardson-Lucy blind deconvolution algorithm
3. CONCLUSIONS
This paper gives a review of different image restoration algorithms. Image restoration is an active research area and various researchers work to improve the efficiency of the different algorithms by developing more efficient algorithms. But primarily image restoration is done mostly using Weiner filter, Richardson-Lucy Blind Deconvolution algorithm, Inverse and Pseudo-inverse filter.
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